The correct interpretation of time-domain or transient electromagnetic (TEM) data relies on effective inversion techniques. Herein, we have developed an effective 3D-TEM inversion method based on the vector finite-element method. The domain was discretized with unstructured tetrahedra to simulate complex geologic structures. We develop a second-order backward-Euler scheme, rigorously with nonuniform time-step sizes, to approximate the time derivative of the electric field. The waveform was directly simulated and considered in the forward modeling and inversion. In a 3D inversion, the most time-consuming element of the workflow is solving a large system of linear equations. To alleviate this problem, we adopt a parallel direct solver for solving a large system of equations involved in forward modeling and sensitivity calculations. We use the Gauss-Newton approach to solve the inverse problem and formulate the least-squares problem to obtain model updates. We avoided the explicit sensitivity calculation by solving the matrix-vector multiplication between the sensitivity matrix (or its transpose) and vector. The developed inversion algorithm is validated using several realistic synthetic models. Finally, we apply the method to practical TEM data with complex topography for coal mine goaf detection. We thus obtain a detailed 3D resistivity model that revealed the layering structure and some localized anomalies related to the coal mine goaf.

In this study, we present an efficient and memory saving 3-D inversion algorithm for interpreting controlled-source electromagnetic (CSEM) data using the total electric field formulation. To tackle CSEM problems involving complex geometries, we discretize the study domain for both forward and inversion problems using unstructured tetrahedral elements. Our inversion scheme combines the parallelized finite element (FE) method with the Gauss–Newton optimal strategy. Additionally, we transform the conventional model space inversion into data space inversion, significantly reducing the computation time and random access memory (RAM) requirements during the inversion process. To begin, we validate the effectiveness and stability of the developed data space inversion algorithm by utilizing a synthetic land CSEM basin model and a synthetic marine CSEM model with bathymetry. These validation experiments further demonstrate that compared with the conventional model space inversion method, the computational efficiency of the data space inversion scheme is greatly improved and the memory required is significantly reduced. Furthermore, we apply the inversion method to survey CSEM data to demonstrate the practical applicability of the new inversion scheme.

The controlled-source electromagnetic (CSEM) method is a crucial tool for near-surface investigations and hydrocarbon exploration because of its economic benefits. Limited resolution is one of the inherent defects of the CSEM method, and to obtain high contrast results a multinary transform function was introduced to CSEM 3-D inversion. The multinary transform function was constituted by superposing several error functions, and the transform function transformed the model parameters from continuously distributed space into a semistep distributed multinary space. To deal with complex geometries, the edge-based finite element (FE) method with an irregular hexahedral grid was applied to the modeling and inverse problem. We used the Gauss–Newton optimization method to minimize the Tikhonov parametric function. The complex chessboard model and the marine CSEM model with complex geometry were used to validate the ability of the new method in improving the resolution of the CSEM method. By comparing the results of conventional, focusing, and multinary inversion methods, the effectiveness of the multinary inversion method in depicting sharp boundaries of different physical properties was proved. Additionally, the comparisons proved that multinary inversion method can, to some extent, overcome the insensitivity to low conductors of the CSEM method.

Efficient 3-D magnetotelluric anisotropy forward modeling is one of the key research techniques used for inversion interpretation. We propose an improved multi-level down-sampling scheme (IMLDS) to reduce the degrees of freedom of the stiffness matrix derived from the edge-based finite element method to improve the computational efficiency, saving on memory usage and calculation time for the forward modeling. Then, to further reduce the memory requirements and speed up the solution of the discretized electric system, we develop a multiple right-hand direct–iterative hybrid solver (MDIHS) based on a block rational Krylov preconditioner. The solver we propose can further save computational costs and time based on the IMLDS. Moreover, the convergence performance of the direct–iterative solver is less affected by the frequency, which solves the problem of slow convergence of the electric field control equation at low frequencies. We also use the high-level language Julia, which is easy to load into third-party packages, to ensure the stability and efficiency of the program. Finally, the validity and advantages of the two schemes are analyzed in detail using three examples. The examples’ results show that the MDIHS and improved multi-level down-sampling can significantly reduce computational memory and save computational time.

We present a regularized inversion method for three-dimensional (3D) magnetotelluric (MT) data with axial anisotropic conductivities based on the edge-based finite element (FE) method. The Gauss–Newton (GN) approach is used to minimize the inversion objective function, including data misfit and regularization penalties, considering both structural complexity and anisotropic penalties. The most time-intensive task in the 3D MT inversion process is solving the large sparse system of linear equations. To speed up the inversion calculation, a hybrid direct–iterative solver combined with a block-diagonal preconditioner that has not yet been applied in anisotropic inversion is developed to accelerate the solutions for the sparse linear system resulting from forward modeling and sensitivity computations. In each GN iteration, a preconditioned conjugate gradient (PCG) method is adopted to overcome the difficulty of the sensitivity matrix storage for the anisotropic scene and obtain a model update without explicitly calculating and storing the sensitivity matrix. Before the inversion test, we use a model to demonstrate that the hybrid solver is computationally beneficial in terms of memory usage and time spent as compared to the direct solver. The good convergence properties and efficiency of the GN–PCG inversion scheme are demonstrated by two synthetic models and USArray data. The proposed inversion scheme can be an important supplement to existing anisotropic inversion algorithms and provide technical support for MT data interpretation.